4.2.2.3. pde.grids.operators.cylindrical_sym module¶
This module implements differential operators on cylindrical grids
make a discretized laplace operator for a cylindrical grid |
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make a discretized gradient operator for a cylindrical grid |
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make a discretized divergence operator for a cylindrical grid |
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make a discretized vector gradient operator for a cylindrical grid |
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make a discretized vector laplace operator for a cylindrical grid |
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make a discretized tensor divergence operator for a cylindrical grid |
- make_divergence(grid)[source]¶
make a discretized divergence operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type
- make_gradient(grid)[source]¶
make a discretized gradient operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type
- make_gradient_squared(grid, central=True)[source]¶
make a discretized gradient squared operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is createdcentral (bool) – Whether a central difference approximation is used for the gradient operator. If this is False, the squared gradient is calculated as the mean of the squared values of the forward and backward derivatives.
- Returns
A function that can be applied to an array of values
- Return type
- make_laplace(grid)[source]¶
make a discretized laplace operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type
- make_tensor_divergence(grid)[source]¶
make a discretized tensor divergence operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type
- make_vector_gradient(grid)[source]¶
make a discretized vector gradient operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type
- make_vector_laplace(grid)[source]¶
make a discretized vector laplace operator for a cylindrical grid
The cylindrical grid assumes polar symmetry, so that fields only depend on the radial coordinate r and the axial coordinate z. Here, the first axis is along the radius, while the second axis is along the axis of the cylinder. The radial discretization is defined as \(r_i = (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\).
- Parameters
grid (
CylindricalSymGrid
) – The grid for which the operator is created- Returns
A function that can be applied to an array of values
- Return type